Keeping this difference in mind, one needs to explicitly check if a unique quantum field (operator) corresponds to a (and only that one) state in the Hilbert space of the theory. We leave this exercise for future work. Such a state-operator correspondence in the `radial-quantization' scheme [1]} was assumed in the literature [2]}, [3]}, in direct analogy with the relativistic CFTs. But, as said in section , in this work we have not performed any radial-quantization. In this context, it is worth noting that, recently in [4]}, it was shown that an alternative quantization scheme named the `angular quantization' of 2D CFT does not give rise to any state-operator correspondence.
